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# How many integers from 1 to 100 are not divisible by 2, 3 and 5?

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Manager
Joined: 11 Sep 2013
Posts: 132
Concentration: Finance, Finance
How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

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Updated on: 27 Oct 2014, 02:34
2
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Difficulty:

75% (hard)

Question Stats:

57% (02:28) correct 43% (02:26) wrong based on 174 sessions

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How many integers from 1 to 100 are not divisible by 2, 3 and 5?

A. 26
B. 29
C. 31
D. 32
E. 41

Originally posted by Raihanuddin on 26 Oct 2014, 12:03.
Last edited by Bunuel on 27 Oct 2014, 02:34, edited 5 times in total.
Renamed the topic and edited the question.
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Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

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26 Oct 2014, 21:27
3
2
Raihanuddin wrote:
Have you got the answer using venn diagram?

The venn diagram doesn't give you the answer directly. You do have to do the calculations shown above.

Numbers divisible by 2 = 50

Numbers divisible by 3 = 33

Numbers divisible by 5 = 20

Numbers divisible by 6 (LCM of 2 & 3) = 16

Numbers divisible by 10 (LCM of 2 & 5) = 10

Numbers divisible by 15 (LCM of 3 & 5) = 6

Numbers divisible by 30 (LCM of 2, 3 & 5) = 3

Total = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(A and C) + n(A and B and C) = 50 + 33 + 20 - 16 - 10 - 6 + 3 = 74

Number not divisible by 2, 3 or 5 = 100 - 74 = 26

You can plug in the same numbers in a venn diagram and solve though using the formula will be more efficient here.
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Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

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Updated on: 26 Oct 2014, 22:14
5
1
7
Raihanuddin wrote:
How may integers from 1 to 100 are not divisible by 2, 3 and 5?
a. 25
b. 29
c. 31
d. 36
e.41

Numbers divisible by 2 = 50

Numbers divisible by 3 = 33

Numbers divisible by 5 = 20

Numbers divisible by 6 (LCM of 2 & 3) = 16

Numbers divisible by 10 (LCM of 2 & 5) = 10

Numbers divisible by 15 (LCM of 3 & 5) = 6

Numbers divisible by 30 (LCM of 2, 3 & 5) = 3

Numbers divisible by 2, 3 & 5 combined = 50 + 33 + 20 - (16 + 10 + 6) + 3 = 103 - 32 + 3 = 106 - 32 = 74

Numbers not divisible by 2, 3 & 5 = 100 - 74 = 26

Is the OA correct OR have I made some mistake?
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Originally posted by PareshGmat on 26 Oct 2014, 20:04.
Last edited by PareshGmat on 26 Oct 2014, 22:14, edited 1 time in total.
##### General Discussion
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Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

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26 Oct 2014, 20:14
1
Raihanuddin wrote:
How may integers from 1 to 100 are not divisible by 2, 3 and 5?
a. 25
b. 29
c. 31
d. 36
e.41

We can take inspiration from Venn diagram as shown below:

Attachment:

ven.png [ 7.11 KiB | Viewed 98674 times ]

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Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

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26 Oct 2014, 21:05
Have you got the answer using venn diagram?
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Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

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26 Oct 2014, 21:41
yes, Karishma is correct.
By using formula we can get the answer easily.

Total = A+B+C -(sum of 2 overlap groups)+(all the three)+Neither
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Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

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26 Oct 2014, 22:18
Raihanuddin wrote:
Have you got the answer using venn diagram?

Its an illustration as pointed out by Karishma.....

Karishma: Thanks for the correction; Kudos to you
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Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

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08 Oct 2016, 05:39
3
2
Hi,

We may also consider that - from 1 to 100 -> 1/2 of the numbers will be divided by 2 and 1/2 will not.
Similarly, from 1-100 -> 1/3 of the numbers will be divided by 3 and 2/3 will not.
And, from 1-100 -> 1/5 of the numbers will be divided by 5 and 4/5 will not.

Hence, No of number which are not divisible by 2,3 and 5 = 100(1/2)(2/3)(4/5) = 80/3 = 26.666. Ignoring the decimal since no of numbers cant be decimal leaves us with 26.
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Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

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20 Nov 2016, 10:55
Raihanuddin wrote:
How many integers from 1 to 100 are not divisible by 2, 3 and 5?

A. 26
B. 29
C. 31
D. 32
E. 41

from 1 to 100, 50 numbers are even, and 50 are odd. therefore, we can eliminate right away 50 numbers.
now...multiples of 5...let's see the multiples of 5 that are not odd...
5, 15, 25, 35, 45, 55, 65, 75, 85, 95 - 10 numbers - another 10 numbers eliminated
multiples of 3 that are not multiples of 5 and are not odd...
3, 9, 21, 27, 33, 39, 51, 57, 63, 69, 81, 87, 93, 99 - another 14 eliminated.
50 - 10 - 14 = 26
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Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

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08 Jul 2017, 09:33
2
1
Such questions are easier to crack if you understand one simple logic -

From 1 to 100 -> 1/n of the numbers will be divisible by n, and (1-1/n) will not - provided n is a prime no.
For example, if we consider, 3(prime) then from 1-100 :
1/3 of the numbers will be divided by 3 and (1-1/3 =2/3) will not be.
Similarly, 1/5 of the numbers will be divided by 5 and 4/5 will not be.

Now this question is a cakewalk -
No of number which are not divisible by 2,3 and 5 = 100*(1/2)*(2/3)*(4/5) = 80/3 = 26.666.
Since, we cant have decimal, ans should be 26.
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How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

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08 Jul 2017, 12:54
Raihanuddin wrote:
How many integers from 1 to 100 are not divisible by 2, 3 and 5?

A. 26
B. 29
C. 31
D. 32
E. 41

can someone help me with my logic here?
If the number of integers from 1 to 100 that ARE divisible by 2, 3 and 5=3, (30, 60 and 90),
then the number of integers NOT divisible by 2, 3 and 5=100-3=97
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Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

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09 Jul 2017, 02:16
gracie wrote:
Raihanuddin wrote:
How many integers from 1 to 100 are not divisible by 2, 3 and 5?

A. 26
B. 29
C. 31
D. 32
E. 41

can someone help me with my logic here?
If the number of integers from 1 to 100 that ARE divisible by 2, 3 and 5=3, (30, 60 and 90),
then the number of integers NOT divisible by 2, 3 and 5=100-3=97

Hi Gracie,
the questions really asks for all numbers that are either divisible by 2, 3 or 5.
This means, 2, 4, 6, 8, ....so on
3, 6, 9, 12, .....
5, 10, 15, 20, ....

Of course LCM (eg- 6, 15, 30, etc ) will be double counted so we must be careful while doing such questions!!
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Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

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Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?   [#permalink] 17 Sep 2019, 23:32
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